Weighted sums of generalized polygonal numbers with coefficients $1$ or $2$
Volume 202 / 2022
Acta Arithmetica 202 (2022), 227-240
MSC: 11E12, 11E25, 11E08.
DOI: 10.4064/aa200630-1-6
Published online: 31 January 2022
Abstract
We consider weighted sums of generalized polygonal numbers with coefficients $1$ or $2$. We show that for any $m\ge 10$, a weighted sum of generalized $m$-gonal numbers represents every non-negative integer if it represents $1$, $m-4$, and $m-2$. Furthermore, we study representations of sums of four generalized polygonal numbers with coefficients $1$ or $2$.
